solve for x : tan-1(2-x/2+x) = 1/2 tan-1x/2
 

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tan-12-x2+x=12tan-1x22tan-12-x2+x=tan-1x2We know that 2tan-1x=tan-12x1-x2Replace x by 2-x2+x2tan-12-x2+x=tan-122-x2+x1-2-x2+x2=tan-122-x2+x2+x2-2-x22+x2=tan-122-x2+x×2+x22+x+2-x×2+x-2+x      a+ba-b=a2-b2=tan-122-x2+x4×2x=tan-14-x24xSo, tan-14-x24x=tan-1x24-x24x=x24-x2=2x23x2=4x=±23
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